Although, theoretically, it is sufficient to take \(n_1 = n = 2\) , several preliminary simulations have shown that \(n_1 = 2n = 4\)  gives better stability in the results. Therefore, for the following simulations, PQC1 takes \(n_1 = 4\)  but still builds a probability distribution over \(2^2 = 4\)  images, by only measuring \(n = 2\)  qubits among four. PQC1 is initialized with an equiprobable superposition over the computational basis, \(\lbrace {0},..., {2^{n_1}-1}\rbrace \)  with \(n_1 = 4\) . Furthermore, the initial parameters for both PQC1 and PQC2 are sampled from a uniform distribution over \([-\delta , \delta ]\) , with \(\delta = 10^{-1}\) . The discriminator is implemented in PyTorch, using an input layer with 4 nodes, two hidden layer with 256, 128 nodes, respectively, and a single node output layer. After the first two layers follows a Leaky ReLU function [1]} with \(\alpha = 0.2\)  and a sigmoid function [2]} is applied after the output layer. In addition, a gradient penalty [3]} for real images is added to help stability and convergence of the model, with the parameters \(\lambda = 7\) , \(k = 0.01\)  and \(c = 1\) .
The dual-PQC GAN is trained using the AMSGRAD optimizer with initial learning rate of \(10^{-4}\)  for PQC1 and discriminator and \(10^{-3}\)  for PQC2.
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